Basic Idea Behind Components

 Last Lecture Make a careful drawing  Today Think carefully about all of the forces Force as a vector Static equilibrium Important Announcement  Problem Solving Tool: Setting up Introduction ! !F = 0 Addition and subtraction on vectors  Important Concepts Chose an axis, put it on your drawing Think carefully about the angles  If you, or anyone you know was advised that you should not take both 8.01L and 18.01A now because they cannot take 8.01L and 18.02A in IAP: THIS IS WRONG!!  Problem Solving Tool: Component checklist Loop through vectors, is there a component? Force is a vector, both magnitude and direction matter Is there an angle factor Vectors: Think with arrows, calculate with components Is is sine or cosine? Many, many students have taken 8.01L and 18.02A during IAP. This is NOT a problem. Is it positive or negative? “Chalkboard” Outline Basic idea behind components  What is a vector?  Want to do a quantitative calculation with vectors  How do you describe a vector?  Need to convert multi-dimensional object to numbers, add or subtract or multiply the numbers, and then generate the multi-dimensional answer  How do you add and subtract vectors?  What does this have to do with forces? F1 F2  Write each vector as a sum of smaller sub-vectors, all of which point in the same direction. Does it move? F3 1 Y Think with arrows… Calculate with components version 1 X Calculate with components version 1 Y X Summary Y X X Y X  Vector: Any quantity characterized by both a magnitude and direction.  Adding or subtracting vectors: Think with arrows, calculate with components. Y Calculate with components version 2  Force is a vector. Calculate with components version 2 First criterion for static equilibrium is that the total force (added as vectors) is zero. 2